For large enough \(n\) 
and \(R_2+R_2^{\prime }<I(U;Y_2)\) , the joint asymptotic equipartition property (AEP)
[1]} implies
\(P_{e,2}^{(n)}& \le \epsilon +T_2 2^{-n[I(U;Y_2)-\epsilon ]} \\& =\epsilon +2^{n(R_2+R^{\prime }_2)}\,2^{-n[I(U;Y_2)-\epsilon ]} \\&\le 2 \epsilon . \) 
